Please help me do this physics problem?

Question

A swing carousel consists of rotating circular platform 11m in diameter (5.5m radius) from which 10 kg seats are suspended at the end of 2.57m massless chains. When the system rotates the chains make an angle of 17.2 degrees with the vertical.

1)what is the speed of each seat? (Answer in units of m/s)
2)If a child of mass 28.8 kg sits in a seat, what is the tension in the chain for the same angle? (answer in units of Newton)

Answer 1

1) The forces on the seat are gravity vertically downward equal to m*g and centripetal force in the horizontal at m*w^2*r where w is the angular speed, and the tension in the chain, T

since the forces must balance when the speed is constant,
m*g=T*sin(72.8)
and
m*w^2*r=T*cos(72.8)
also v=w/r
m*v^2/r=T*cos(72.8)

dividing the first equation by the second
g*r/(v^2)=tan(72.8)

solving for v
v=sqrt(g*r/tan(72.8)

4.36 m/s
(using g=9.81)

the r is 5.5m+2.57*sin(17.2)

2. Use either equation to find the tension with m=10+28.8

398 N

I used the angle at the horizontal, which is 90-17.2, or 72.8
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